Problem: Express this quotient in scientific notation: ${\frac{4.500\times 10^{5}} {9.0\times 10^{5}}}$
Answer: Start by collecting like terms together. $= {\frac{4.500} {9.0}} \times{\frac{10^{5}} {10^{5}}}$ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= 0.50 \times 10^{5\,-\,5}$ $= 0.50 \times 10^{0}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$ . In this case, we need to move the decimal one position to the right without changing the value of our answer. $ $ We can use the fact that $0.50$ is the same as $5.00 \div 10$ , or $5.00 \times 10^{-1}$ $ = {5.00 \times 10^{-1}} \times 10^{0} $ $= 5.00\times 10^{-1}$